x^2-152x-40=0

Solution for x^2-152x-40=0 equation:

x^2-152x-40=0

a = 1; b = -152; c = -40;
Δ = b2-4ac
Δ = -1522-4·1·(-40)
Δ = 23264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23264}=\sqrt{16*1454}=\sqrt{16}*\sqrt{1454}=4\sqrt{1454}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-4\sqrt{1454}}{2*1}=\frac{152-4\sqrt{1454}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+4\sqrt{1454}}{2*1}=\frac{152+4\sqrt{1454}}{2}
$